Question

Из двух населенных пунктов, находящихся на расстоянии 2,5 км одновременно в одну сторону начинают двигаться автомобиль и мотоцикл. Скорость автомобиля 20 км/ч, а мотоцикл 10 км/ч. Через какое время автомобиль догонит мотоцикл? ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

Запишем уравнения движения автомобиля и мотоцикла:

x₁= V₀₁*t
x₂= 2,5 + V₀₂*t

Поскольку автомобиль догнал мотоциклиста, то
x₁=x₂
20*t = 2,5+10*t
10*t = 2,5
t = 0,25 часа или 15 минут

Answer 2

Problem Analysis

We are given that a car and a motorcycle start moving simultaneously from two different locations that are 2.5 km apart. The car has a speed of 20 km/h, and the motorcycle has a speed of 10 km/h. We need to determine the time it takes for the car to catch up to the motorcycle.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the car and the motorcycle is the difference between their speeds. In this case, the relative speed is 20 km/h - 10 km/h = 10 km/h.

We know that the distance between the car and the motorcycle is 2.5 km. To catch up to the motorcycle, the car needs to cover this distance. We can use the formula:

Time = Distance / Speed

Substituting the values, we have:

Time = 2.5 km / 10 km/h

Simplifying, we get:

Time = 0.25 hours

Therefore, it will take the car 0.25 hours to catch up to the motorcycle.

Answer

The car will catch up to the motorcycle in 0.25 hours.

Explanation

When the car and the motorcycle start moving simultaneously, the car is faster than the motorcycle. Therefore, it will gradually close the distance between them. After 0.25 hours, the car will have covered a distance of 5 km (20 km/h * 0.25 h), which is equal to the initial distance between them. At this point, the car will have caught up to the motorcycle.

I hope this helps! Let me know if you have any further questions.